Apparatus for measuring the mode quality of a laser beam

ABSTRACT

A method and apparatus for determining the quality of a multimode laser beam (10). In the preferred embodiment, the apparatus includes a lens (32) for creating a transformed or imaged waist from the input beam. The location of the transformed beam waist and its diameter are then determined. These steps can be carried out by chopping the beam using a rotating hub (34) having apertures (36,38) for selectively passing the beam. Preferably, one of the apertures has a pair of 45° knife edges (40,42). The transmission of the beam past the knife edge is monitored by a detector (30). In operation, the lens focal position is varied while the transmission of the beam past the knife edge is monitored in order to locate and measure the diameter of the transformed waist. The diameter of the beam at one other known location is measured. A processor then calculates beam quality by fitting these measurements to a mathematical model. Once the quality of the beam is calculated, the location of the original beam waist and its diameter can be derived. Once all of the beam parameters are derived, the propagation characteristics of the beam can be predicted.

This is a divisional of application Ser. No. 07/344,980, filed Apr. 27,1989, now U.S. Pat. No. 5,100,231.

TECHNICAL FIELD

The subject invention relates to a device for measuring the mode qualityof a laser beam and specifying the propagation constants for themeasured beam.

BACKGROUND OF THE INVENTION

One of the principal distinctions between ordinary light and laser lightis related to beam propagation. Ordinary light may be thought of as theaggregate sum of a large number of individual spherical electromagneticwaves each radiating from its own separate point source (called Huygen'swavelets in optics textbooks). The individual sources making up theemitter act independently without correlation in space, time orfrequency between the individual waves. A familiar consequence, taughtin traditional optics texts, is that if one uses a lens to collect suchlight and concentrate it as tightly as possible in the lens focal plane,the best result is an illuminated region that is the composite image ofall the individual incoherent sources with a surface brightness nogreater than the surface brightness of the source. The size of thisilluminated area will grow in proportion to the size of the emitter andany attempt to create higher intensity in the focal spot by increasingthe size (and total power radiated) of the emitter will proveunsuccessful. In contrast, laser light can be characterized as a singlewavetrain (or a small number of wavetrains) having uniform frequency andphase over a broad space transverse to the propagation direction. Suchcoherent light can be concentrated by a lens to a diameter that can beas small as the Heisenberg uncertainty principle allows (i.e., focusedto the "diffraction limit"), regardless of the spatial extent of thesource.

The way in which intensity is distributed across the laser beam hasimportant consequences in the degree to which a small focal-spotdiameter can be achieved. A beam comprising a single wavetrain with aGaussian intensity distribution (shown as the TEM₀₀ mode profile inFIG. 1) will focus more tightly than any other distribution. SuchGaussian beams can be produced by lasers, but typically at a significantsacrifice in output power. Lasers employ resonant cavities to storeoptical energy, and this energy is stored in various "modes", each withits own frequency and distribution of intensity. The mode of lowestorder is the one that has the Gaussian intensity distribution justdescribed, and is for that same reason, the mode that occupies thesmallest diameter inside the laser resonator. Higher order modes havemore complex intensity distributions and occupy larger cross-sectionalareas.

The mode profiles of FIG. 1 are used as examples throughout and so arehere briefly explained. For each mode, the intensity in the beam(vertical axis) is plotted as a function of the radial distance outward(horizontal axis) transverse to the beam propagation axis. Thisintensity could be measured, for example, by detecting the powertransmitted through a small pinhole aperture (one with an opening smallcompared to the beam width) as the pinhole was moved across the beamperpendicular to the propagation axis. The characteristic radius of theTEM₀₀ mode is used for the units for the horizontal axis, where thedefinition of this characteristic radius is the conventional "1/e²radius" as explained later. The mode designations TEM_(p1) are given incylindrical coordinates, for radially symmetric intensity profiles(there are similar-looking, but different designations for rectangularcoordinates, so the coordinate system must be specified). The units ofthe intensity axis are relative but normalized so that the same power iscontained in each of the modes. The mode order--essentially the numberof nodes in the profile, which determines the rate at which the beamspreads--increases by one with each plot, stepping down in FIG. 1, theTEM₀₀ mode being the lowest order mode, TEM₀₁ * being the next highest,etc.; these are the six cylindrical modes of lowest order. The modes areshown with the correct relative scales to be a set of higher order modesgenerated by one laser, in one resonator. A mixed mode profile is madeup by summing these profiles (or even higher order profiles) with weightfactors proportional to the relative power of that mode in the mixture.For example, adding the first three profiles together would make a modeprofile that peaked in the center and was without radial nodes; thiswould resemble the TEM₀₀ mode but would always propagate with a largerdiameter. Modes are useful concepts not only because these intensityprofiles are generated by real lasers but because these profiles(including mixed mode profiles) remain unchanged as the laser beampropagates or is focused. Since the same profiles apply at the focus ofa lens, the figure indicates the relative scale of how tightly each modefrom a given laser can be focused.

It is generally possible to constrain any laser to operate only in thefundamental (TEM₀₀) mode by reducing the diameter of the limitingaperture in the laser cavity, thereby increasing the optical loss suchthat no mode except the TEM₀₀ mode experiences sufficient net gain tooscillate. The price for this is lower power in the output beam than ifseveral modes were oscillating. Laser manufacturers usually choose tocompromise between the two competing goals, high power and TEM₀₀ mode,by using designs that allow some power in the higher order modes. Theintensity distributions for these mixtures of modes can appear to beGaussian, but they do not propagate or focus with as small a transverseextent as the pure TEM₀₀ mode would.

The fact that a laser beam can have a Gaussian-like intensitydistribution, but yet have the higher power possible only with amixed-modes, has led some laser manufacturers to improperly claim thattheir products generate pure TEM₀₀ beams. In fact their products producebeams that are a mixture of higher order modes, with an intensityprofile that only superficially resembles a fundamental mode profile.This has lead to unrealized expectations, often with great economicconsequences, for unwary designers of laser systems and naive laserusers. An important factor which has allowed these problems to continuehas been the absence of a simple, easy-to-use, low-cost instrument forquantifying beam quality in a meaningful way. An even more fundamentalproblem has been the lack of a theoretical basis for a meaningful way toquantify beam quality. A related issue is that while there exists muchinformation about how to compute the propagation of TEM₀₀ beams, thereis no practical set of analytical "tools" with which to predict theattributes of a mixedmode beam as it propagates through an opticalsystem. It is these analytical tools and the resulting instrumentationfor quantifying beam quality which are the subjects of this invention.

The absence of an analytical description for the propagation of themixtures of higher order modes that come out of real lasers makes itvery difficult to design optical beam delivery systems which mustchannel these multimode beams through a plurality of optical elements toa workpiece. In an industrial laser beam delivery system, selecting theproper elements is extremely important. For example, the final deliverylens is typically very close to the workpiece, and often becomescontaminated from material removed from the workpiece. Due to thiscontamination, the final delivery lens must be replaced very frequently,sometimes many times a day. These lenses can be quite expensive.Moreover, the cost of these lenses goes up significantly with theirsize. Accordingly it is desirable to design a beam delivery system wherethe optical elements are as small as possible while still being capableof passing the beam. This requires knowledge of the propagationcharacteristics of the higher order mode beam. It would be best to havean analytical model that would show how to optimally prepare the beamout of the laser for launch into the delivery system so as to minimizethe cost of the whole system.

At present, there are only very crude methods available for designingoptical delivery systems for industrial lasers. In one approach, thelaser beam is directed across a room, over a distance equivalent to thatwhich will be used in the commercial application. This distance can bemany meters. Technicians will then insert pieces of plastic at variouslocations in the beam path. The burn hole created in each piece ofplastic can be used to give information about the diameter of the beamand the intensity distribution pattern at that location. In addition tobeing crude, this latter approach is dangerous because the technicianand other employees must move around a room though which a mulitkilowattinvisible beam is being transmitted. It would clearly be desirable tohave an improved way of determining the mode quality or mixture of modesin a laser beam.

As noted above, most laser beams, and particularly those generated byhigh power commercial lasers, are comprised of a mixture of higher ordermodes. For the purposes of designing optical elements, it has been foundthat a detailed knowledge of all the underlying modes is unnecessary.Rather, as will be shown, the propagation of a multimode laser beamthrough an optical system can be predicted if one can characterize thebeam by a numerical "quality". This quality number will turn out to bethe same figure as "times-diffraction-limit" figure known in opticsliterature and it is the factor by which the focus-spot diameter for ahigh-order beam is larger than that for a TEM₀₀ beam having the samediameter at the focussing optic. Equivalently, it is the factor by whichthe angle of spreading, or divergence angle, for a high order mode isincreased over a diffraction-limited, TEM₀₀ mode beam of the same waistdiameter.

FIG. 2 illustrates a high order mode or multimode laser beam 10propagating along an axis 12. The beam converges to a smallest diameter14 (perpendicular to the axis) called the waist of value 2W_(o), andthen diverges propagating away from the waist location. In a distance ofpropagation Z_(R) on either side of the waist called the Rayleigh range16, the beam diameter is larger by a factor of √2 than the waistdiameter. This means the beam cross-sectional area has doubled.

Within this beam is drawn a representation of the beam propagation ofthe fundamental mode 18 of Gaussian intensity profile which has the samewaist location as the multimode beam 10, and a Rayleigh range 20(propagation distance for the area of this beam to double) given thelower case symbol z_(R) of the same value as beam 10, or z_(R) =Z_(R).The beam 18 with these properties will be termed the "associatedfundamental mode" for the multimode beam 10. The laws of diffractiondictate that a beam of waist diameter A will spread at large distancesfrom the waist with a divergence angle inversely proportional to thewaist diameter and proportional to the wavelength λ of the light, or

    (divergence)=(constant)(λ/A)                        (1)

The proportionality constant depends on the intensity distributionacross the beam and the way the beam diameter is defined. The smallestpossible constant occurs for a fundamental mode with a Gaussianintensity profile I(r,z) given by

    I(r,z)=I.sub.o exp[-2r.sup.2 /(w(z))].sup.2                ( 2)

where I_(o) =2P/πw² and is the intensity at the center of the beam, P isthe total power in the beam, r is the radial distance from the centerand w(z) is a radial scale parameter which increases with distance zaway from the waist.

If the beam diameter is taken as twice the radius for which theintensity has dropped to 1/e² =13.5% of the central intensity, then2w(z) is the beam diameter at distance z, and the constant in thedivergence expression for this fundamental mode is 4/π. The laws ofdiffraction relate the Rayleigh range for a fundamental mode to thewaist radius by the expression:

    z.sub.R =πw.sub.o.sup.2 /λ                       (3)

so that for the beam 18 the waist diameter 22 is equal to:

    2w.sub.o =2(λz.sub.R /π).sup.1/2                 ( 4)

and the far field divergence angle 24 is

    θ.sub.F =(4/π)(λ/2w.sub.o) or 4λ/(π2w.sub.o)(5)

Equation (5) is equivalent to equation (1) with the "constant" expressedas (4/π).

The divergence angle Θ_(F) (shown at 26 in FIG. 2) for the multimodebeam 10 is greater than for the associated fundamental mode beam 18 by aconstant factor M equal to:

    Θ.sub.F =Mθ.sub.F                              ( 6)

where the value of M depends on the definition of beam diameter used forthe multimode beam. Given these definitions, the laws of lightpropagation give that the beam diameter 2W(z) for beam 10 is everywherejust M times larger than that for the associated fundamental mode, or

    W(z)=Mw(z)                                                 (7)

and in particular the waists of the two beams are related by

    2W.sub.o =2Mw.sub.o                                        ( 8)

To characterize the propagation of the multimode beam, the factor bywhich its divergence angle, Θ_(F), exceeds the divergence angle of aTEM₀₀ beam having the same waist diameter must be determined. A TEM₀₀mode having a waist diameter of 2W_(o) will diverge more slowly than thesmaller associated fundamental mode according to:

    4λ/π(2W.sub.o)=4λ/πM(2w.sub.o)=θ.sub.F /M(9)

The "quality" of the multimode beam is just the ratio of its divergence,Mθ_(F) to that for a TEM₀₀ of the same waist diameter expressed in (9).This ratio is seen to be Mθ_(F) /(θ_(F) /M) or M². Thus, M² is thequantity which characterizes the quality of beam 10 wherein smallervalues represent a higher beam quality.

This definition leads to a number of observations. First, a beam that isa pure fundamental mode has an M² value of 1. Second, as the value of M²increases, the divergence of the beam increases and quality decreases.Most importantly, analytical tools can be developed for predicting thepropagation of a multimode laser beam if the value of M², 2W_(o) and thewaist location are known. (The equation for beam propagation of a higherorder mode beam is shown below at (11).)

All modes generated in a given laser resonator, have the same radii ofcurvature and propagate with the same characteristic distance (Rayleighrange) for the beam area to double, regardless of the mode order, as iswell known in the literature (see e.g., H. Koglenik and T. Li, AppliedOptics, Vol. 5, Oct. 1966, pages 1550-1567). The associated fundamentalmode was defined by matching its Rayleigh range to that of the multimodebeam. This means the associated fundamental mode found above is the sameTEM₀₀ mode that would be generated and appear in the ensemble of modescomprising a multimode beam for that resonator. Each pure higher-ordermode making up the multimode beam is everywhere along the z-axis, largerthan this underlying TEM₀₀ mode by a constant factor; and so thediameter of the entire sum-of-modes is everywhere larger by the constantfactor M. This makes Equation (7) true for multimode laser beams, and byso identifying the associated fundamental mode, a propagation law(equation 11) for the multimode beam is obtained by appropriateinsertion of the M-factor in the well-known propagation law for thefundamental mode.

To identify the associated fundamental mode, the Rayleigh range of themultimode beam must be measured, requiring measurement of the locationof the beam waist, and a minimum of two beam diameters at knowndistances from the waist. When this data is fitted to the modifiedpropagation law to give the values of 2Wo, M², and the location Z_(o) ofthe beam waist, the desired analytical model of multimode beampropagation is achieved. Equation 11 becomes the mathematical tool thatprovides the ability to model and predict beam diameter and wavefrontcurvature at any location in an optical system for multimode beams. Raymatrix methods, for example, become as useful for high mode-order beamsas Koglenik and Li showed them to be in the reference cited above forfundamental mode beams.

While it is possible to predict the propagation of a laser beam if thevalue of M², waist diameter and location can be determined, there is nodevice presently existing which can adequately measure these parameters.At best, researchers have been limited to measuring the profiles ofbeams at a plurality of locations to obtain an empirical feel for modequality. Information about beam profiles can be obtained by burningplastic blocks as discussed above. Much more sophisticated beamprofilers are available which can give information about the energydistribution of a beam at a location in space. However, informationabout beam diameter or energy distribution at a one location does notprovide enough data to derive a value for M² or the other parameters.Therefore it would be desirable to have an apparatus which can directlymeasure the model parameters for a multimode laser beam.

An apparatus for measuring the mode quality of a beam will have manyuses beyond designing beam delivery systems. For example, manyscientific experiments require that the beam quality be at or near theunity value of the fundamental mode. Such an apparatus can be used tomeasure beam quality as the laser resonator mirrors are peaked inangular alignment so that the TEM₀₀ mode output can be maximized.

Other uses of the subject invention will include the pinpointing ofmisadjusted or imperfect elements in an optical train. Morespecifically, since the quality of a beam will be degraded when passedthrough an imperfect optical element, by comparing the beam quality bothbefore and after passing through a particular optic, information can bederived about the optic itself. The subject apparatus can also behelpful in reproducing experimental results that depend on the modemixture of the input multimode beam.

Accordingly, it is an object of the subject invention to provide amethod and apparatus for determining the quality of a laser beam.

It is another object of the subject invention to provide an apparatuswhich can determine beam quality at a single location near the output ofthe laser.

It is still another object of the subject invention to provide a methodfor optimum design of laser beam delivery systems based on knowledge ofthe mode quality of a laser beam.

It is still a further object of the subject invention to provide anapparatus which can generate information about the alignment of a laserbeam.

It is still another object of the subject invention to provide anapparatus which generates information about the pointing stability of alaser.

It is still a further object of the subject invention to provide anapparatus for generating improved beam profiles.

It is still another object of the subject invention to provide anapparatus which can generate information about the underlying modesforming a multimode laser beam.

SUMMARY OF THE INVENTION

In accordance with these and many other objects, a method and apparatusis disclosed which is suitable for measuring the mode quality of a laserbeam. This result requires a fit of the multimode beam parameters to theanalytical model based on measuring the multimode beam's Rayleigh range.The form of the multimode beam propagation equation dictates that ahigher accuracy fit to measured data results if one of the beamdiameters measured is at or near the multimode beam waist.Unfortunately, the actual beam waist may be located many meters awayfrom the output coupler of the generating laser and therefore may berelatively inaccessible for measurements. Also, the beam waist may belocated within the laser resonator and, if so, it could not be accesseddirectly at all.

To overcome this problem, the subject apparatus includes a lens forcreating a transformed or imaged beam waist. The apparatus is arrangedto determine the location of this transformed waist, and measure thediameter of the beam at two locations a known distance from this waistlocation, thus giving the Rayleigh range. A processor is provided tocalculate a value for beam quality based upon the location of thetransformed beam waist and the two measured beam diameters. Once themode quality of the beam is known, the original beam waist location andits diameter can be calculated using the model equations and the knownfocal length of the lens.

In one embodiment of the subject invention, the transformed waist islocated by adjusting the position of the lens with respect to a meansfor measuring the beam diameter. The distance between the lens and themeasuring means when the beam diameter is at its smallest is used todefine the transformed waist location.

In another embodiment, the transformed waist location is determined bymeasuring the diameter of the beam at locations on either side of thetransformed waist. When the beam diameters are equal at the twolocations, the beam waist will be equidistant between the two locations.

In either case, once the location of the transformed waist isdetermined, it is desirable to measure the beam diameter at that waistlocation. The diameter of the beam is also measured at another knownlocation which is preferably spaced from the transformed waist adistance greater than the Rayleigh range of the transformed beam.

In the prior art, there have been developed a number of devices formeasuring beam diameter. Most of these devices will generally producesimilar values for a beam diameter when measuring a beam that isprincipally in the fundamental mode. However, when dealing with higherorder mode beams, there has not been developed a generally accepteddefinition of beam diameter. Accordingly, the instruments available formeasuring beam diameter will generate different results depending uponthe definition being used. It should be understood that the subjectinvention could be implemented with any definition of higher order beamdiameter. The calculated value for beam quality would of course bedependent on the definition chosen for beam diameter.

In the preferred method for carrying out the subject invention, adefinition of beam diameter is suggested that has advantages both from ameasurement standpoint as well as from a theoretical standpoint. Theseadvantages will be discussed in greater detail below with respect to thepreferred embodiment.

In the preferred apparatus of the subject invention, beam diameter isdetermined utilizing a rotatable hub located in the path of the laserbeam. The hub is provided with a plurality of apertures for selectivelypassing and chopping the beam. A detector is provided on the other sideof the hub for measuring the variations in the intensity of the beam asit passes though the hub.

In the preferred embodiment, at least one of the apertures includes aknife edge disposed at a 45 degree angle with respect to the plane ofrotation of the hub. As the beam is passed by the knife edge, theintensity measured at the detector will rise from zero to the maximum(complete transmission). Assuming the speed of rotation of the hub isknown, the diameter of the beam can be measured by the rise time of theintensity signal generated by the detector. A very suitable beamdiameter can be calculated if the times between transmitted fractions ofthe total beam power are used when most of the change in the transmittedpower occurs, such as the time between the 1/5 and 4/5ths total powerpoints. In this manner, any of the light energy that is weaklydistributed in higher order modes will not falsely exaggerate thediameter of the beam.

In the preferred embodiment, two knife edges are provided, both at 45degrees with respect to the plane of rotation of the hub and orthogonalto each other. Two knife edges are provided to permit measurement ofbeam diameter and mode quality along two orthogonal axes. Thismeasurement is desirable because these parameters vary with respect tothe azimuth angle around the beam propagation axis. A minimum andmaximum of beam diameter and mode quality will be found for intensityprofiles as a function of azimuth angle and these extremes willgenerally be for azimuths orthogonally oriented. In this embodiment, ameans is provided for changing the plane of rotation of the hub withrespect to the azimuth around the propagation direction of the beam sothe knife edges can be aligned with the maxima and minima for variousmode patterns. Separate values for beam parameters, including M², can becalculated for each axis.

In operation, the beam is focused by the lens to create a transformedwaist near the rear hub plane. In one approach, the position of the lensis varied while the diameter of the beam is measured at the rear of thehub. When a minimum is detected, the beam waist will have been locatedat this rear plane. In another approach, the position the lens is varieduntil the beam diameter at both the front and rear of the hub are thesame. This serves to accurately locate the transformed waist at thecenter of the hub. The position of the lens can then be moved by half ahub diameter closer to the hub to position the transformed waistaccurately at the rear of the hub where it can be measured. The beamdiameter is also measured on the front side of the hub which is a fixedknown distance (i.e. the diameter of the hub) away from the waist. Fromthis information, the processor can fit the measurements to theanalytical model and calculate a value for M². As noted above, theprocessor can also calculate the location of the original input beamwaist and diameter from the known focal length of the lens and the knowndistance between the lens and the imaging planes of the hub. All of thisdata can then be used to predict the propagation of the beam.

The subject device can also provide information in addition to the modelbeam parameters. For example, the use of a knife edge allows thetransverse position of the beam relative to the apparatus to be located.More specifically, when the knife edge is at the center of the beam, thedetector will measure a transmission level of 50 percent. Since thismeasurement can be made at two spaced apart locations, namely, the frontand the rear plane of the hub, information about beam pointing andalignment can be derived.

Information about the profile of the beam can also be generated. Oneapproach can include differentiating the signal from the detector as theknife edge cuts the beam. This information will correspond to the typegenerated in prior art profilers using slit apertures.

Another approach to obtain beam profile information would be to includea pinhole in the hub. When a pinhole is passed by the beam, the varyingintensity measured at the detector will give a picture of the beamprofile. This approach has been used with only limited success in theprior art because it is necessary to accurately align the center of thebeam with the track or scan line of the moving pinhole. This difficultyis overcome in the subject invention because the knife edge apertures inthe hub can be used to accurately align the pinhole scan line throughthe center of the beam.

After a pinhole profile has been taken and stored in the memory of theapparatus, this information can be analyzed by the processor foradditional results. In particular, the mean location of the intensitydistribution can be computed, as well as the second moment of thedistribution about the mean location. The latter quantity is of interestas a mathematically attractive method of defining the diameter of ahigher order mode (as the root-mean-square diameter) and the modequality of a higher order mode (as the normalized second moment).

One advantage of obtaining a beam profile using the subject invention isthat a profile taken close to the output coupler can be made relativelyfree of distortions caused by diffraction from the limiting aperture inthe laser resonator. This result is achieved because the focusing lenswill tend to focus the overlaid diffraction pattern at a distance fromthe transformed waist generally greater than a Rayleigh range for theimaged beam. Thus, if the profile is taken at the transformed waist, aneffective far-field profile is generated even if the apparatus is in alocation close enough to the laser to be considered in the near field ofthe original beam.

In the preferred embodiment, a slide member having a stationary pinholeaperture of known diameter is provided which can be selectivelyintroduced over the center of the hub. Using the beam locating featuresof the two 45 degree knife edges, the beam propagation axis can bepositioned over the center of the hub, to intersect the pinhole. Thelens can be positioned to place the imaged beam waist at the pinhole aswell. Thus when the hub is turned to give nominally 100% transmission ofthe beam (as it is with the beam between the two 45 degree knife edges),introduction of the stationary pinhole will give the transmission of thebeam through the known pinhole diameter under standardized conditions.This is of interest as a direct measure of the ability of a multimodebeam to be focused to a small spot.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1F are drawings illustrating the normalized intensitydistributions for the first six lowest order modes of a cylindricallaser resonator.

FIG. 2 is a drawing of a laser beam illustrating the relationshipbetween a multimode beam and the underlying fundamental mode quantities.The particular fundamental mode illustrated is defined in the text andis termed the associated fundamental mode.

FIGS. 3(a), 3(b), 4(a), 4(b), 5(a), 5(b), and 6A-6D illustrate four modeprofiles and their cross-sections, and are used in a discussion ofalternative ways to define the diameter of a higher order mode.

FIGS. 7(a)-7(d) are simplified perspective views of an apparatus formedin accordance with the subject invention showing a focused beam beingchopped by an angled knife edge aperture in the front and rear aperturepositions.

FIGS. 8(a)-8(c) are a series of time-sequenced drawings illustrating thechopping of a beam with a knife edge.

FIG. 9 is a graph illustrating the transmission curve that would begenerated based on the chopping of a beam by a knife edge as shown inFIG. 8.

FIG. 10 is a graph, similar to FIG. 9, showing the transmission curvethat would be generated based on scanning the other knife edge past thebeam in a manner to successively expose the beam.

FIGS. 11(a)-11(c) are graphs illustrating the measured transmissioncurves for various laser modes.

FIG. 12 is a graph illustrating the knife edge transmission curves forthe mode of FIG. 6.

FIGS. 13(a) and 13(b) are drawings illustrating how beam positioninformation can be derived using a knife edge aperture.

FIG. 14 shows the change in the measured diameter of a laser beam as thelens-aperture distance is varied.

FIG. 15 is a simplified cross-sectional view illustrating the effect oftranslating the lens in accordance with the subject invention.

FIG. 16 is an exploded perspective view of the first embodiment of thesubject invention.

FIG. 17 is an enlarged perspective view of the device shown in FIG. 16and illustrating the approach for providing six axes of adjustment toallow alignment of the beam with the subject apparatus.

FIG. 18 is a perspective view of the hub used in the first embodiment ofthe subject invention.

FIG. 19 is an illustration of a display that might be used to relay theinformation generated by the device of the subject invention to theuser.

FIG. 20 is a simplified perspective view of the first alternateembodiment of the subject invention.

FIG. 21 is a simplified perspective view of the second alternateembodiment of the subject invention.

FIG. 22 is a schematic view of a gantry delivery system utilized to scana laser beam over a workpiece.

FIG. 23 is a schematic view illustrating how the diameter of the opticalelements in a fixed delivery system can be minimized with the knowledgeof beam quality.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Prior to discussing the details of the subject invention, somebackground on the propagation of beams as a function of beam quality,and measurement of beam diameters will first be given.

Higher Order Mode Propagation

The multimode beam propagation law resulting from considerations of theassociated fundamental mode can be obtained by substitution of themultimode beam quantities, through Equations (7) and (8), into thefundamental mode law from the literature; and the relation of matchedRayleigh ranges:

    Z.sub.R =z.sub.R =πw.sub.o.sup.2 /λ=πW.sub.o.sup.2 /M.sup.2 λ                                                  (10)

The result is an expression containing quantities that are allmeasurable as properties of the multimode beam. In general the locationof the waist along the propagation axis is not known precisely untilthese measurements are done. For convenience the zero point along this,the z-axis, is initially chosen arbitrarily and the waist locationassigned the value z_(o), making the propagation distance in thepropagation law z-z_(o). Thus for a multimode beam of quality M² :##EQU1## where W_(o) is the beam radius at the waist, located at z_(o),and W(z) is the radius of the beam at location z.

While many laser beams are circularly symmetric about their propagationaxis like the beams discussed so far, in general a beam can haveindependent propagation constants in two planes each containing thez-axis and perpendicular to each other, as is well known in theliterature. That is, the propagation equations must in general allow forthe possibility of astigmatic beams, with elliptical cross-sections.This means there are two equations of the form (11) to be fitted fromdiameter measurements in the two principal planes (the two planescontaining the maximum and minimum diameters of the elliptical crosssection). The apparatus described below allows beam diameters to bemeasured along any azimuth direction (diameter) of the beam crosssection, to facilitate finding the principal planes, and facilitate thetaking of the required measurements. Measurements in a singlepropagation plane are discussed first, applicable directly to asymmetric beam or one principal plane of an asymmetric one, followedlater by a discussion of methods for handling astigmatic beams.

Assuming that the wavelength λ is known, equation (11) has threeunknowns, namely, the diameter of the waist of the higher order mode(2W_(o)), the location of the beam waist (z_(o)) and the value of M².Thus, three independent measurements of a multimode beam must be takento determine the three unknown constants in equation (11). These threemeasurements can be the beam diameters at three separate propagationdistances from the waist.

For greatest accuracy, it is preferable that the three measurementsinclude a positive location of the waist position (z_(o)) and ameasurement of the beam waist diameter (2W_(o)). Positive location ofthe beam waist position (z_(o)) is best done by making beam diametermeasurements on both sides of the waist position. Because the beamdiameter does not vary significantly at various positions near thewaist, attempts to locate the waist by extrapolating diameter data takenon only one side of the waist will be relatively inaccurate. Theresulting error in the determination of M², for example, will be twiceas large on a percentage basis, as the fractional error in (z-z_(o)).This occurs because the term (z-z_(o)) is squared in equation 11. Thesubject apparatus is designed to rapidly and easily make accuratemeasurements for determining mode quality, including locating the beamwaist with diameter measurements on both sides of the waist.

Measurement of Beam Diameters

As pointed out above, in order to obtain a value for M² using equation(11) it is necessary to take measurements of beam diameter. Anymeasurement must be based upon a suitable definition of beam diameter. Asuitable and widely accepted definition for beam diameter is availablefor a TEM₀₀ fundamental mode beam. However, there is no widely accepteddefinition for beams of higher order modes. The difficulty can best beunderstood by referring to FIGS. 3 through 6 below.

FIG. 3 is an illustration of a fundamental mode beam, shown in profilein FIG. 3a and in cross-section in FIG. 3b. The cross-sections for allof FIGS. 3 to 6 cut across the profiles at heights which are at 13.5% ofthe height of the central peak. The intensity profile of FIG. 3a isacross a horizontal center line x-x' transverse to the propagation axisand passing through the center of the beam as shown in FIG. 3b. As canbe seen, FIG. 3a represents the lowest order mode Gaussian intensitydistribution. As previously explained, the beam diameter is thereforedefined as the width between the points where the intensity of the beamdrops to the 1/e² or 13.5% of the peak intensity. These cutpoints areshown as crosses in FIG. 3a, and the beam diameter labeled there as2W_(o). The value of M² is 1 for this pure TEM₀₀ mode beam, which couldrepresent the beam 18 of FIG. 2.

There are many commercially available devices which can take ameasurement of beam diameter using this definition. One type of priorart device manufactured by both Datascan and Dataray (the latter underthe trademark Beamscope), uses a motor to move an arm carrying a slitoverlaid on a detector through a beam. The light passing through theslit is measured by the detector. The slit is oriented perpendicularlyto the direction of motion. When the slit is moved across the beam shownin FIG. 3b, the detector will generate an intensity signal versustranslation distance comparable to the trace shown in FIG. 3a. Inoperation, this signal is stored in memory and from this information aprocessor can determine the maximum signal and calculate the locationswhere the 13.5% clip levels occurred. The processor can then calculatethe beam diameter based on the distance the arm moves between these twolocations.

Another commercially available device is marketed by Photon Inc. underthe trademark BeamScan. In this device, a rotating hub is placed in thepath of the laser beam. The rim of the hub includes at least oneaperture, such as a slit or pinhole, which is moved past the beam as thehub rotates. A photodetector protrudes into the space encircled by therim of the hub, and is aligned with the beam. The output of thephotodetector will generate a trace similar to FIG. 3a. The maximum(100%) signal level is found on an initial revolution of the hub, andthe distance the aperture moves between the 13.5% clip levels during thesubsequent rotation is measured and displayed as the beam diameter.

A third device, marketed by ALL under the trademark Laser Beam Analyzer,uses a spinning wire to slice through the beam. Reflections off the wireas it passes through the beam are measured by photodetectors. Onceagain, the outputs of the photodetectors will generate traces similar toFIG. 3a. The diameter of the beam can be derived using clip levels andthe known motion of the wire as described above.

Measuring beam diameters becomes more complex as the laser beam modesbecome more complex. FIG. 4 illustrates a laser beam having one radialnode and no azimuthal nodes. This mode is referred to in the literatureas the TEM₁₀ mode in cylindrical coordinates. This mode pattern includesa high intensity central zone and a second concentric zone of lesserintensity located radially outside the center zone. A scan with apinhole aperture will give an intensity profile through the center ofsuch a beam is shown in FIG. 4a. The width of this beam can be takenfrom this profile using the same definition as for the TEM₀₀ beamdiscussed above.

The cross-sectional cut at the 1/e² height produces three radii for thismode as shown in FIG. 4b, but it seems reasonable to take the outermostone (labeled 2W₁ in FIG. 4) in extending the fundamental mode diameterdefinition to this mode. The value of M² for this beam would be 2.26with this definition. (Note that the modes of FIGS. 3, 4, 5 are takenfrom FIG. 1 and retain the horizontal axis labeled in units of radii ofthe associated fundamental mode. Thus the square of horizontalcoordinate gives the M² value for each diameter determination.)

Difficulties with this definition become apparent, however, when anextension to the TEM₂₀ mode of FIG. 5 is attempted. This mode has noazimuthal nodes, and two radial nodes. When cut at the 13.5% height, theoutermost peak of the profile (occurring at the radius indicated by thedashed line in FIG. 5b) is just missed (the height of this peak is atabout 12%). Thus the diameter 2W₃ of the outermost radius of the crosssection is less than the diameter 2W₁ just found for the lower orderTEM₁₀ mode. In fact 2W₃ is very nearly the same as the diameter of thefundamental mode (FIG. 3) while this mode has clearly much higherdivergence and is of much lower quality.

Furthermore, an adequate definition must deal with mixed modes, not justthe pure higher order modes considered so far. The percentages of themodes in a mixture can vary continuously, and as a smaller diameter,lower order mode is mixed in with a higher order mode, a continuouslydecreasing diameter should result. But consider what would happen if asmall percentage of the TEM₁₁ * mode from FIG. 1 were mixed with theTEM₂₀ mode. Since the nodal radii of the two modes do not coincide, thefirst effect would be that the amplitudes of the depressions in thedominant TEM₂₀ mode profile would begin to fill in, and no longer reachzero. The peak height of the mixture would remain the same, since theTEM₁₁ * mode being added in has a node at the center, where the dominantmode has a peak. This means that the 13.5% clip level would remain atthe level drawn in FIG. 5a. But the height of the outermost peak,contributed to the mixture by the TEM₂₀ mode, would rise and exceed the13.5% clip level at about an admixture fraction of 20% in the TEM₁₁ *mode. Based on the present definition, the beam diameter for the mixturewould thus increase discontinuously near this percentage from about 2W₃to about the diameter of the dashed circle of FIG. 5b, changing not onlydiscontinuously but in the opposite direction to what is reasonable forthe mixing in of a lower order mode.

Similarly, the inverse effect of a discontinuous jump to smaller valueswould occur when mixing into the TEM₁₀ mode a roughly equal proportionof the TEM₂₀ mode (adding the profile of FIG. 5a to FIG. 4a). This woulddouble the height of the central peak while leaving the region at the2W₁ diameter of FIG. 4a little changed, since the TEM₂₀ mode has a nodenear this diameter. The result would be that the new 13.5% clip levelwould be above and miss the TEM₁₀ outermost peak, and the beam diameterwould jump from 2W₁ to a smaller value based on clipping the combinedcentral peaks.

To avoid these difficulties, a higher order mode diameter definition wasintroduced in the literature based on the radius at which the intensitydropped to 1/e² of the intensity of the outermost peak (Freiberg andHalsted, Applied Optics, Vol. 8 (Feb. 1969), pp. 355-362). This newdefinition can be said to reduce to the standard definition for thefundamental mode, where there is only one peak. This new definitionwould give the result 2W₂, for example, for the diameter of the mode ofFIG. 4a, or an M² with this definition of 3.65 instead of the value of2.26 for the TEM₁₀ mode given by the first definition. Thus, it can beseen that the actual value of M² depends on the selection of thedefinition of the higher order mode beam diameter. The beam profile doesnot change; the definition merely picks the feature to which the beamwidth will be measured (see the discussion in W. Bridges, AppliedOptics, Vol. 14, Oct. ' 75, pages 2346-47). If a wider feature is chosen(as in the second definition) equation (11) correctly gives a widerdiameter. The difficulties with this second definition become apparentby examining FIG. 6.

An adequate definition must deal with asymmetric modes such as the TEM₂₀mode in rectangular coordinates of FIG. 6 as well as the circularlysymmetric modes dealt with in FIGS. 3-5. FIG. 6 shows a cross-sectionand three pinhole profiles along the indicated paths at differentazimuthal angles for this rectangular coordinate mode, which has twonodes in the horizontal plane and none vertically. Using either thefirst or the second definition above there is a discontinuity in beamdiameter as the azimuth angle of the scan is continuously varied. Thescan along A-A' in the major diameter 2W₄. As the scan line azimuthangle swings around towards the minor principal plane (scan B-B' hasswung about 1/8 of the way or thirty degrees) the outermost peak heightsdecrease as the pinhole now traverses the flank of the outer lobes ofthe mode. The scan B-B' produces the diameter 2W₅ by the firstdefinition, and a slightly larger diameter results with the seconddefinition. When the azimuth angle has reached the scan C-C' at sixtydegrees, the profile peaks from the outer lobes of the mode have almostdisappeared. The result is that the diameter given by the firstdefinition has suffered a discontinuous jump down to 2W₆, while thediameter by the second definition has been pushed out to beyond thewidth of the profile displayed in the figure. Finally, when the scanreaches the minor principal plane D-D', there are no profile peaks fromthe outer lobes of the mode (the profile looks like C-C' with the lowouter peaks removed) and the diameter by the second definition jumpsdiscontinuously to a value of about the 2W₆ diameter of the figure. Ascan be seen, there are significant difficulties with the presentdefinitions of beam diameter. Measurements taken at scan angles nearthese discontinuities would be highly unstable and subject to large andrapid fluctuations. This situation is unacceptable in most measurementdevices. As will be seen below, the subject invention overcomes theseproblems.

Preferred Methods of Measuring Beam Diameter

Discontinuities in the measured beam diameter can be avoided if themeasurement (and definition) of the higher order mode diameter is basedon an integration over the whole cross sectional area of the beam, andaccount is taken of the total power in the beam. In the preferredembodiment this is done in one of two ways. In the first method, theintensity distribution would be recorded from a pinhole scan of the beam(or equivalent means). A processor would then use this information tocompute the second moment of the intensity distribution. This approachis discussed in greater detail below in the section on additionalcomputational capabilities of the instrument.

In the second method, the power transmitted past a knife edged aperturescanned through the beam is measured. FIGS. 7 and 8 illustrate thesecond method. The elements shown in FIGS. 7 and 8 constitute the maincomponents of the preferred embodiment of the subject invention. As seentherein, beam 10 is aligned with a detector 30. Detector 30 is arrangedto measure the power of the beam transmitted past the knife edge. Toperform this function, the detector must be sufficiently large so thatall of the beam falls on its active surface. The choice of detector willdepend on the wavelength of the laser beam. In FIG. 7, a lens 32 is usedto create a transformed or imaged waist as discussed in further detailbelow.

Before the beam reaches the detector 30 it will pass by a rotating hub34. As used here, a hub is a support means for carrying an aperturethrough the beam at a fixed distance from a rotation axis. Convenientlyfor mechanical balance this means may have a shape like the hubsupporting an automobile tire, hence the use of the term. Hub 34includes two apertures 36 and 38. Aperture 38 acts as a window forpassing light and therefore can have any suitable configuration.Aperture 36 includes two edges 40 and 42 each inclined at 45° withrespect to the plane of rotation of hub 34. Edges 40 and 42 are alsoorthogonal to each other. The signal generated by the detector 30 as thebeam 10 is cut by either knife edge can be used to provide a measure ofbeam diameter.

FIG. 8 illustrates a sequence viewed from the detector 30 where edge 42cuts beam 10 as in FIG. 7B. FIG. 9 illustrates the output of thedetector at a time corresponding to the position of the hub with respectto the beam in FIG. 8. At a time t_(A), as shown in FIG. 8A, the edge 42is just approaching the beam. The beam is entirely transmitted throughthe hub so that full power is reaching the detector and the signaloutput is 100%.

At time t_(B), shown in FIG. 8B, the edge 40 has cut part of the beamand reduced the light energy reaching the detector. The transmittedpower reaching the detector will continue to decrease monotonically asthe hub continues its rotation in the direction indicated by the arrow.At time t_(C), shown in FIG. 8C, half of the beam has been blocked. Attime t_(D), shown in FIG. 8D, most of the beam is blocked and at timet_(E), shown in FIG. 8E, none of the beam power is reaching thedetector.

As shown in FIG. 8, times can be conveniently measured as the elapsedtime following the passing of a fiducial mark, here shown as a notch 44located on the rim of the hub, past a means to read the mark, here shownas an optical interrupter 46. The rim of the hub is moved at a constant,known velocity V, so that multiplication of these times by V convertsthem to the distance the aperture has moved.

The power transmitted past a knife edge can be used to measure thediameter of the beam. This concept has been used in the literature formeasuring beam diameters of pure TEM₀₀ modes and small admixtures of thenext few higher order modes with the fundamental mode (distorted TEM₀₀modes). It has been found that this concept can be extended with goodresults for measuring beam diameters of multimode beams.

It is reasonable to require that the definition adopted for higher ordermode diameters, produce the conventional 1/e² diameter for the TEM₀₀mode when applied to the fundamental mode. The transmission of a TEM₀₀mode past a knife edge positioned a distance y/w beam radii from thecenter of the beam is well known in the literature (see e.g., Cohen etal., Applied Optics, Vol. 23, Feb. 15, 1984, pp. 637-640) and is givenby: ##EQU2## The function erf(x) is the error function of probabilitytheory, tabulated in mathematical handbooks. Equation (12) gives for thecutting of a fundamental mode beam as in FIG. 8 a falling, S-shapedcurve as in FIG. 9, with the property that the distance moved betweenthe 15.8% and 84.2% transmission points is precisely one beam radius w.The transmission of a higher order mode past a knife edge produces anS-shaped curve as well that is very similar to the one for thefundamental mode. A suitable definition for the diameter of a higherorder mode is twice the distance between these same cut levels on thissimilar S-shaped curve. Thus, it can be seen that the width of the beamcan be measured by looking at the time elapsed between the detection ofclip levels set at 15.8% and 84.2% (hereinafter referred to as 16% and84% for brevity). Twice the elapsed time (2(t_(D) -t_(B)) in FIG. 9) ismultiplied by the velocity of the rim of the hub 34 to derive thediameter of the beam.

The calculation above is accurate for a knife edge that is oriented withits edge perpendicular to the plane of rotation of the hub. Such anorientation is perfectly acceptable if one is only interested inmeasuring the beam diameter in one plane. However, if information aboutbeam diameters along two perpendicular axes is desired, two knife edgesoriented at 45° to the plane of rotation should be used.

The effect of using a knife edge is to create a scan across the beamalong a line perpendicular to that edge. This is also true when theknife edge is at an angle with respect to the plane of rotation of thesupport. This can be visualized by viewing FIGS. 8B through 8D where itwill be seen that the beam is progressively covered from the upper leftcorner to the lower right corner. Because the scan is taken at an anglewith respect to hub rotation, the effective speed of the scan (i.e., thespeed of the perpendicular motion), is less than the velocity of the rimof the hub which supports the knife edge. Therefore a correction factormust be utilized to calculate the beam diameter. This correction factoris given by sin 45° or 1/√2 (=0.707) for a 45° knife edge. Thus, thebeam diameter will be given by the time elapsed between the 16% and 84%clip levels times the rim velocity reduced by a factor of 0.707.

The output of the detector 30 generated when beam 10 is progressivelyuncovered by edge 40 is shown in FIG. 10. Given the direction of motionof the hub as depicted in FIG. 8, this will not occur until the hub hasmoved through enough of one revolution such that edge 40 is brought backaround to the beam. Just prior to edge 40 crossing the beam, no power istransmitted to the detector. As the hub continues to rotate, the beamwill be exposed and the power transmitted to the detector 30 isincreased in a manner exactly inverse to the blocking of the beampreviously described with respect to edge 42. This output provides ascan across the beam perpendicular to the edge 40. Since the two edges40, 42 are perpendicular to each other, edge 42 provides a scan acrossthe beam extending perpendicular the scan generated by edge 40. Itshould be noted that beam 10 shown in FIG. 8 is a symmetric TEM₀₀ modesuch that both scans have the same character and generate the same valuefor beam diameter and M². This will not be the case for asymmetricbeams, as discussed below.

The concept of generating perpendicular scans using apertures disposedat 45° angles with respect to the rotation of the hub has been used inthe prior art BeamScan device mentioned above. In the latter device, twoslits, disposed at 45° angles with respect to the rotation of the hubare used. In addition, in the BeamScan device, the entire hub assemblyis mounted in a collet permitting the assembly to be rotated about aline parallel to the plane of rotation of the hub. When the axis of thecollet is aligned along the propagation axis of the incoming beam, ascan through any azimuth angle in the cross-section of the beam can bemade. The ability to orient the plane of rotation of the hub to takescans as a function of azimuth is a desirable feature which isincorporated in the preferred embodiment of the subject invention asdiscussed below.

The principal advantage of using the power transmitted past a knife edgeto measure beam diameter is the fact that the signal rises monotonicallyfor both the TEM₀₀ mode and all higher order modes regardless of thepeaks in the mode profile. As the knife edge uncovers the beam, thetransmitted power signal can only increase as more of the beam isexposed to the detector. For beam diameters measured between clip pointson this signal, this fact eliminates the diameter discontinuity problemsdiscussed with the earlier methods of beam diameter measurement. FIG. 11shows the transmission signal past a knife edge measured for threebeams, a pure TEM₀₀ mode beam, a nearly pure TEM₀₁ * mode beam, and amixed-mode beam containing roughly equal parts of the TEM₀₁ * mode andthe TEM₁₀ mode (with a small fraction of TEM₀₀ mode in addition). Thesemode designations are all in cylindrical coordinates and correspond tothe designations of FIG. 1. The pinhole profile for the 90% TEM₀₁ * modeof FIG. 11B, looked like the profile for that mode in FIG. 1 except thatthe central node dipped down to 14% of the peak height instead ofreaching 0%. The pinhole scan of the mixed mode of FIG. 11C looked likethe TEM₁₀ mode profile of FIG. 1, except that the nodal dips were at 63%of the central peak height, and the outermost peaks were at 79% of thecentral peak height. The modes measured in FIG. 11 were generated in anargon ion laser (Coherent Innova Model 90-6, with non-standardshort-radius cavity optics) with an internal mode-limiting aperturewhose diameter could be varied. By opening this aperture, the higherorder mixed modes were generated. By closing the aperture (and reducingthe discharge current through the laser tube) the pure TEM₀₀ mode couldbe generated, FIG. 11A. Thus, the mode of FIG. 11A is the "associatedfundamental mode" which goes with the modes of FIG. 11B, 11C.

As can be seen, the transmission patterns for all the modes areS-shaped. As the mode pattern becomes more complex, the curve becomesstraighter in the middle and the outer edges turn over faster.

Reasonable values for beam diameters can be generated for all modes. Thebeam radii W determined by the 16% and 84% cut points for each of theFIG. 11A, B and C modes are taken from the bottom scale showing themotion of the knife edge and are 1.22 mm, 1.89 mm and 2.20 mm,respectively. Since in this example FIG. 11A is the associatedfundamental mode for the set of modes of the figure, the M² values forthese modes are obtained as the square of the ratios of the B and Cdiameters to the A diameter, or M² is 1, 2.40 and 3.25 for the modes ofFIG. 11A, B and C.

Moreover, this approach eliminates the sharp discontinuities in measuredbeam diameter values that would be generated as one varied the azimuthangle of the scan on the beam cross section while measuring the diameterof the beam, as illustrated in FIG. 12. FIG. 12 illustrates computedtransmission functions for the mode shown in FIG. 6, as the knife edge40 uncovers the beam, scanning perpendicular to the edge from A to A',etc., as indicated by the arrows. The shape of the A-A' scan along themajor principal diameter for this mode is readily understood. Along thisdiameter there is a nodal line between each lobe of the mode, alignedwith the knife edge. As each lobe is uncovered by the knife edge, itgenerates the characteristic S-shaped pattern for a single spot, ofheight proportional to the total power in that lobe, with the patternsfor the three lobes stacked on each other.

When the scan direction azimuth is moved to B-B', the upper part of theknife edge begins to uncover the upper part of the central lobe, beforethe edge is clear of the lower part of the left-most outer lobe. Thusthe "step" in the transmission pattern is smoothed out, the "tread"becomes inclined without a horizontal portion. This process continuesuntil at C-C' the steps have almost disappeared, and the beam widthindicated has narrowed towards the value of the minor principaldiameter. The profile along D-D' is a smooth S-shaped curve withoutsteps, similar to FIG. 11A. The measured beam diameters decreasesmoothly in this sequence with no discontinuities. Thus, this approachis ideally suited to determining mode quality of beams since it producesconsistent results for beams of any quality.

In addition to providing a good definition of beam diameter, there areseveral other advantages in using a knife edge. First, with a knife edgethere are no deconvolution errors which occur with pinholes or slits. Adeconvolution error refers to the fact that with a pinhole or a slit,the profile width that is measured has a component due to the width ofthe pinhole or slit as well as the beam width; the transmission signalis a convolution of the two widths. This error is not serious so long asthe aperture width is much less than the beam width. For a fundamentalmode profile, aperture widths up to 1/6 of the beam width for a pinhole,and up to 1/9 of the beam width for a slit, will add to the measuredwidth an error of no more than 1% of the true beam width. For largeraperture widths a mathematical deconvolution should be done to correctthe measured profile, which is difficult for an arbitrary mixed mode.Thus, pinhole and slit apertures cannot be used with tightly focusedbeams.

A knife edge has no width, and adds no convolution error to the measuredtransmission signal so long as the edge is the mathematically straightline assumed in calculating the transmission past the edge. Thisproperty means that a knife edge can be used for all focal diameters onthe scale of which the edge is straight. It is not difficult to getstraight edges on a scale on the order of ten microns--ordinary razorblades are this straight.

The knife edge technique also provides a transmission signal that has agood signal to noise ratio in the measurement of beam diameters. Theimproved signal is a result of the fact that the knife edge is straightline, of dissimilar symmetry to the limiting aperture in the laserresonator, which is generally circular. The limiting aperture creates adiffraction pattern with circular symmetry which overlaps with the mainlaser mode near the laser. The two patterns (the mode and thediffraction pattern) suffer optical interference with each other, whichmeans a circular pattern of fringes is superposed on the laser mode asdescribed in the literature (See Siegman, Lasers, University ScienceBooks, Mill Valley, Calif., 1986). These fringes move erratically withmicrophonic motions of the limiting aperture relative to the main lasermode, and create noise on detectors measuring a partially obscured beam.With the signal transmitted past a knife edge, however, due to thesymmetry difference there are always both bright and dark interferencefringes going past the edge, which average out and reduce this noise.

Another advantage of using a knife edge is that powers on the order ofthe full beam power are detected. Detected light signals are generallyless noisy if more light is detected. As can be appreciated, a slit willtransmit significantly less power than a knife edge aperture. The powertransmitted by a pinhole is even less.

Another advantage for using a knife edge is that it can be used to giveinformation about the position of the beam. More specifically, the 50%transmission point defines the center of the beam being detected. Thetiming of these 50% transmission points, as the beam is cut in a hubrotation by knife edges 40 and 42, gives the position of the beam centerrelative to these edges. The knife edges move at constant velocity V. Ifthe beam center is on the centerline of the knife-edged window shown inFIG. 13A, and the distance between edges along the centerline is L, thenthe time difference between uncovering the center of the beam by theedge 40, and the blocking of the center of the beam by edge 42, will beL/V. If the beam center is above the centerline by an amount H₁, thedistance between the 50% cut points is L-2H₁ (for edges at 45° to thescan direction) as may be seen in FIG. 13A. Thus a time difference 2H₁/V shorter than L/V, as shown in FIG. 13B indicates a beam center heightH₁ above the centerline. Similarly, a time difference 2H₂ /V longer thanL/V between 50% points (FIG. 13B) indicates a beam center height H₂below the centerline, when the edges 40, 42 are oriented as in FIG. 13A.Once the height in the window of the beam center is known, the beamcenter position along the scan direction is given by the timingdifference between the 50% point time at either knife edge and the knownrotation position of the hub. The rotation position of the hub is knownbased on the time t_(B) elapsed since the passage of the fiducial mark44 through the interrupter 46, and the distance between the fiducialmark and the edge of the knife at the known height (see FIG. 13A). Forexample, for a beam center on the centerline, the distance from the edge42 to the fiducial mark is shown in FIG. 13A as L₁.

As can be appreciated, these two distance measurements L₁ and either H₁or H₂, locate the position of the beam within the knife edge aperturewindow. Since locating the beam center position depends only on thetiming difference between the 50% transmission points at the two knifeedges (relative to the known timing difference along the centerline), itcan be seen that window geometries other than FIG. 13 will work as wellif their timing differences are known.

One benefit of this position information is that it can be used to alignthe propagation axis of the beam with the optical axis of the instrumentduring the M² measurement. Having a reproducible means to insure beamalignment, insures reproducible beam quality measurements. Beamalignment is also critical where a pinhole is to be used to generatebeam profiles. More specifically, if a pinhole is not accurately alignedthrough the center of a multimode beam, an inaccurate profile will begenerated.

Another advantage to having a sensitive means for detecting beamposition is that fact that the stability of the pointing direction ofthe laser beam can also be monitored. As discussed below, in thepreferred embodiment, transmission information is taken from the knifeedges as they intersect the beam both when they are near the lens as inFIGS. 7A and 7B, called the front position, and when they have beenrotated away from the lens as in FIGS. 7C and 7D, called the rearposition. By generating two-dimensional transverse beam positioninginformation at two spaced apart locations, the input beam angulardirection (relative to the instrument) can derived. The size of thefluctuations in this input direction determines the beam pointingstability.

The one drawback to using a knife edge is that it generates curves asshown in FIGS. 9 through 12 rather than the profiles of FIGS. 1 and 3through 6. Profiles such as would be obtained with a slit can begenerated from the transmission signal past a knife edge if thattransmission signal is differentiated with respect to the edge motion.This was demonstrated by J. A. Arnuad et al, Appl. Optics, Vol 10, pg2775, Dec. 1971. In the preferred embodiment discussed below, a profileis generated separately with a pinhole in order to obtain the fullheights of the intensity peaks and the full depths of the nulls, withoutthe averaging inherent in a slit profile.

Measurement of Mode Quality M²

As discussed above, in order to model the propagation of a multimodebeam using Equation (11), one needs to make three independentmeasurements. While these three measurements can theoretically be thebeam diameter at any three independent locations, these measurementsmight require extreme precision to accurately locate the beam waist, dueto the form of the multimode propagation equation (11) mentionedpreviously. If the measurements are taken far away from the beam waist,in the asymptotic limit of the beam, the separate effects of the modequality, waist diameter, and waist location in determining the beamdivergence can not be accurately isolated from each other.

This problem can be overcome if measurements are taken at or near thebeam waist. However, the beam waist is often relatively inaccessible.For example, the waist can be located many meters from the laser orinside the resonator structure.

Therefore, in accordance with the subject invention, measurement of modequality is most practically carried out by using a focusing means, suchas a lens or mirror, to create a transformed waist which is easilyaccessible to direct measurement. A means is then provided for locatingthe transformed beam waist. Once the beam waist is located, at least twomeasurements of beam diameter are taken. Preferably, one of thosemeasurements is at the beam waist. Once these three measurements arecompleted, a value for M² can be calculated. Based on the focal lengthof the lens, the location of the transformed waist and the calculatedvalue for M² ; the location of the original beam waist and its diametercan also be calculated. With this information, the propagation of thebeam can be predicted, including the determination of the original beamwaist diameter and location.

In order to carry out this method, a means must be provided to measurebeam diameter. There are a number of devices presently available tocarry out such a measurement. FIGS. 7 and 15 illustrate one preferredembodiment containing the basic elements for carrying out the subjectinvention.

As discussed above, the subject device includes a lens 32 for focusing abeam and creating a transformed waist. The beam is aligned with detector30. A rotating hub 34 having at least two apertures 36 and 38 intersectsthe beam. As the hub rotates, the transmission past the knife edges 40and 42 is monitored at both the front and rear positions of the knifeedges. These output signals can be used to give measurements of beamdiameters at these two positions.

In practice, the first step would include aligning the beam usinginformation about the 50% transmission signal as discussed above.Additional details regarding the method for aligning the beam withrespect to the preferred embodiment will be discussed below. Once thebeam is aligned, the most accurate measurement of M² can be derived.

After the beam is aligned, the waist is located There are two methodsfor performing this step. Both of the methods rely on the fact that theposition of the waist can be moved if the lens position is moved.Accordingly, a means must be provided for translating the lens and forkeeping track of the lens position. The transformed waist location,relative to the lens, is given by well-known expressions in theliterature (see the Kogelnik and Li reference cited above). Typicallythe input waist location will be a meter or more away from theinstrument, and the focal length of the lens will be much less than thedistance to the input waist. Under these conditions, the transformedwaist will lie a little beyond one focal length away from the lens andwill stay approximately at that distance away as the lens is moved. Inany event, the transformed waist position moves with the lens position,and the processor in the instrument can be programed to account for theslight non-linearly between these two motions once the beam parametershave been measured at any lens position.

In the first method for locating the waist, the lens position is variedin order to place the waist at the rear knife edge position. This resultis achieved by monitoring the transmission past the knife edge 40 as thelens is translated. The beam diameter is calculated for each rotation ofthe hub based on the time difference between the 16% and 84%transmission levels. As noted above, the time difference is easilyconverted into beam width since the speed of rotation of the hub isknown.

FIG. 14 shows a plot of measured beam diameters taken as the distancefrom the aperture position to the lens is varied. When curve 60 hits thelowest value, the beam waist has been located at z_(o). The valueobtained at that location is the diameter of the transformed waist andis used in the subsequent calculation for M².

For simplicity of discussion, only the scan along one axis (edge 40)will be described at this point. In the preferred embodiment, a two axisscan is performed using both knife edges 40, 42. It should also be notedthe 100% transmission value used to set the clip levels is continuouslyupdated on each hub rotation and used for the following pass of theknife edge.

Once the beam waist is located and its diameter measured, the diameterof the beam at another location is determined. This determination ismost easily obtained by taking a measurement at the front position ofthe aperture as shown in FIG. 7A. The advantage of obtaining the secondbeam diameter measurement at this location is that it is a preciselyknown distance from the previously measured transformed waist, namelythe diameter D of the circle drawn by the aperture in a full rotation,which as noted above is being referred to as the diameter of the hub.The measurement of the second beam diameter is performed by detectingthe time difference between the 16% and 84% transmission levels asdiscussed above.

After these three measurements have been taken, the value of M² can becalculated using the following equation:

    M.sup.2 =(πW.sub.o /2λ)Θ.sub.F             (13)

where ##EQU3## is the full multimode beam divergence angle shown in FIG.2 and where 2W_(o) is the transformed beam diameter measured at thewaist, 2W_(o) is the diameter of the transformed beam measured at thefront aperture position, D is the diameter of the hub, and λ is thewavelength of the laser beam.

Once the value of M² is known, the diameter of the original beam waist(2W_(o)|in) and its distance from the lens (Z_(in)) can be calculatedwith the following formulas: ##EQU4## where Z_(R) is the Rayleigh rangegiven by:

    Z.sub.R =πW.sub.o.sup.2 /M.sup.2 λ               (17)

where d is the distance from the front aperture position to the lens,and f is the focal length of the lens. As noted above, once M², theoriginal beam waist diameter 2W_(o)|in and its location Z_(in) areknown, equation (11) can be used to predict the propagation of the beam.

The second method of locating the beam waist includes measuring the beamdiameter at two locations on either side of the waist. When the diameterat these two locations is equal, the waist will be located exactlybetween the two locations.

This method is readily carried out in the subject invention. Morespecifically, lens 32 is moved in a manner to locate the waist somewherewithin the hub. The beam diameters at both the front and the rearaperture positions are continuously measured. The position of the lensis then adjusted until the diameters measured at both positions areequal. This is shown as the dotted lens position 32' in thecross-section of the device shown in FIG. 15. At this point, it is knownthat the waist is located midway between the two aperture positions atthe center of rotation 48 of the hub 34 in FIG. 15.

This method is more accurate than the first approach. The reason forthis greater accuracy can be appreciated by referring to FIG. 14 whichillustrates the variation of beam diameter with respect to thelens-aperture distance. As can be seen, the rate of change of beamdiameter is much smaller near the waist than at locations about aRayleigh range of the transformed beam away from the beam waist. Thus,the change in diameter for any given movement of the lens can bemaximized if a measurement location is selected away from the waist. Asthe rate of change is increased, the measurement accuracy is increased.

Curve 60 also shows that the change in beam diameter varies equally oneither side of the waist. Thus, if two locations are found to have thesame diameter on either side of the waist, the waist will be foundequidistant between the two locations.

Once the waist is located in this manner, the lens can be translated anamount D/2 to place the waist at the rear aperture position. At thispoint, the same measurements as discussed above are taken. Morespecifically, the diameter of the waist is measured at the rear apertureposition. In addition, the diameter of the beam at the front apertureposition is measured. With these measurements, the value of M², theoriginal beam waist diameter 2W_(o)|in and its location Z_(in) can becalculated using equations (15) and (16). The propagation of the beamcan then by predicted using equation (11).

Using the latter method of locating the beam waist requires that thelens be capable of moving at least a distance D/2. This increaseddistance will increase the size of the device and add some costs.However, it is believed that the precision with which the waist can belocated using the latter method is enhanced by roughly an order ofmagnitude. This improvement comes not only from the fact that the rateof change of diameter with position increases away from the waist, butthat the detection of the equality of the two beam diameters (by rapidlysampling and comparing the measurements made at the front and rearaperture positions and driving the difference to zero) is inherentlymore accurate than attempting to sequentially measure two absolutenumbers.

As noted above, in the latter method, the waist is first located at thecenter of the hub. Thereafter, the lens is moved in a manner to placethe waist at the rear aperture position. Due to the slight divergence ofthe incoming beam, if the lens is moved an amount D/2, the transformedwaist location will not move exactly the distance D/2 due to the slightnon-linearity between these two motions. This second order inaccuracycan be corrected by programming the processor to iteratively compute thecorrection for the non-linearity after the input beam parameters aremeasured at the first position, move the lens to the corrected position,and repeat the process until the computed correction is negligible.

The waist locating sequences described above occur at start-up, when theprocessor moves the lens through a wide enough range to initially findthe transformed beam waist. When this sequence is completed, theprocessor servos the lens in a dither-and-track steady state operationto always hold the transformed waist at the rear aperture position (evenif the input waist location moves). To do this, the processor steps thelens a small amount first to one side of the last known waist location,and then steps back through the middle to the other side, and measuresthese rear position beam diameters for each step. As long as the waistis located at the rear position, the end stepped diameters will both belarger than the middle step. If an end step diameter is smaller than themiddle step diameter, the processor moves the lens in the small diameterstep direction to restore the desired "middle diameter the smallest"condition--this is the tracking part of the operation of the lens servo.From the initial beam parameter information gathered on start-up andsubsequently updated, the processor can compute a suitable step size.This would be a step just large enough to make a detectable change inthe stepped diameter over the waist diameter (a change of about 1% ofthe waist diameter). For the beam of FIG. 14, this makes the dither stepmotion of the lens a distance of about 0.005 inches (1/8 mm).

Two Axis Measurement

As discussed above, providing aperture 36 with two opposed 45° knifeedges allows the beam cross-section to be scanned along two orthogonaldiameters. In the preferred embodiment, the azimuthal angle of theinstrument can be varied around the incoming beam axis such that thescan axes generated by the two knife edges will be aligned with themaximum and minimum principal diameters of the beam.

For the most accurate measurement of a beam in a principal plane, thetransformed waist is placed (and held in place by the steady-state lensservo) at the rear aperture position. This presents a problem if theinput beam has very different waist locations for the two principalplanes (i.e., the input beam is astigmatic). In this case, thetransformed waists will also be located at different distances from thelens, and the lens can only be positioned properly for one of theprincipal planes. This situation is managed by using the input beaminformation gathered by the processor on both principal planes duringthe start-up lens-focusing sequence. The processor compares subsequentvalues to the initial ones to determine when a large enough change hasoccurred to require refocusing to keep the displayed measurements validwithin the specified accuracy of the instrument. Because the instrumentis constantly monitoring beam diameters in both principal planes, theprocessor can decide when such a large change has occurred even in thenon-servoed plane.

Typical operation with an astigmatic beam is illustrated as follows. Oninitial start-up the processor moves the lens over a range large enoughto locate the waist positions and measure the diameter at the waists andfront aperture positions for both principal planes. This tells theinstrument the input beam parameters for both principal planes at thetime of start-up.

Often the user of the instrument is more interested in the changes inthe beam parameters for one of the principal planes than the other; thisplane can be user selected to be the primary plane (defined as the onedriving lens servo) or the default setting of the instrument for theprimary plane can be accepted. Most laser beams are not highlyastigmatic and acceptable readings of beam parameters, at somewhat loweraccuracy, are obtained from the beam diameters measured in the (slightlyout of focus) secondary principal plane. The instrument displays thereadings for both principal planes, but highlights the ones for the moreaccurate primary plane, in this case of a slightly astigmatic inputbeam.

For large astigmatism in the input (and transformed) beam, theinstrument is forced to sequentially switch between the two principalplanes, alternately bringing each into focus, by switching control ofthe lens servo, to maintain the instrument's accuracy. This switchingcan be done manually by the user or the user can select an automaticmode where each principal axis (whose output readings are highlighted).is alternately selected by the processor for a few seconds ofmeasurement. The measurements made during the last "in-control" cycleare remembered and displayed by the processor (but are dimmed on thedisplay) during the other-axis measurement cycle.

The processor can decide and prompt the user as to when alternatingoperation is necessary, based on two criteria. Both the diameter andslope of the diameter versus lens focus curve (like FIG. 14) areavailable from measurements in the secondary principal plane. (These areavailable even though the lens is being servoed for and stepped at astep size computed for the primary principal plane, because bothprincipal diameters are always being measured.) Reasonable criteriawould be if the secondary mode diameter changes by more than 5%, or theslope of the secondary diameter curve versus step size changes by morethan 20%, of their respective initial values. In this case, the user isgiven a prompt that the alternating-focus operation is necessary.

First Principal Embodiment

FIGS. 16 and 17 show the first principle embodiment 100 of the subjectinvention. This device includes a rotating hub 134 for chopping thelaser beam 10. A lens 132 is provided for creating a transformed waist.The position of the lens is adjustable along arrows A in FIG. 17 asdiscussed below. The transmission of the beam past the hub is measuredby detector element 130.

As seen in the Figures, the lens, hub and detector are mounted on asupport stand 150 designed to allow the orientation of the hub withrespect to the beam to be adjusted such that the beam can be accuratelyaligned for measurement. There are many different designs available fora support stand to satisfy this requirement.

In the illustrated embodiment, the support stand 150 includes a base 152and a vertical post 154. A hub support platform 156 is mounted to thepost 154 via clamp 158. Vertical adjustment (along arrows B in FIG. 17)is achieved by moving clamp along post 154 after the set screw 160 hasbeen loosened.

The lateral movement along the horizontal axis is provided by anadjustment screw and plate combination (162,164). By rotating screw 164,the position of the hub support platform is adjusted along the axisshown by arrows C in FIG. 17.

As noted above, it is desirable to be able to adjust the plane ofrotation of the hub with respect to the propagation axis of the beam inorder to scan along various azimuth angles. This adjustment feature isprovided by rotational element driven by lever 170. The rotationalelement (not shown) is connected directly to the hub and permits 110° ofrotation about the beam axis along arrows D.

Angular tilt adjustability is provided by tilt plate 180. Tilt plate 180is similar in construction to well known mirror adjustment structures.The tilt plate 180 is spring loaded (springs not shown) to the hubsupport platform 156 to give a compressive load against screws 182 and184. By adjusting screw 182, the vertical tilt of the hub with respectto the beam can be varied as shown by arrows F. Adjustment of screw 184will vary the horizontal tilt as shown by arrows E. Arrows A-Fillustrate the six degrees of motion afforded by this design.

Lens 132 is a low aberration lens and is selected based on thewavelength of light being tested. To facilitate operation, it would bedesirable to include with each lens some form of ROM chip having thelens parameters, such as focal length, stored therein. This permits theuse of interchangeable lenses, as calibration information on the lenscan be read directly by the processor to facilitate the calculation ofthe various beam parameters. The lens focal length is chosen to givetransformed beam characteristics (divergence, waist diameter) that canbe conveniently measured, for the range of input beam parameters theinstrument is designed to measure. Examples of design parameters forseveral wavelength ranges are given below.

A suitable means for translating the lens and keeping track of itsposition is required As shown in FIG. 17, a stepper motor 186 can beused. In order to first locate the waist in the center of the hub, andthen move the waist to the rear aperture position, the lens must be ableto move a distance about equal to its focal length.

As noted above, detector 30 functions to measure the transmitted powerof the beam. The selection of the detector will be based on thewavelength of the laser beam. For example, a silicon photodetector willmeasure light having a wavelength between 0.2 and 1.0 microns and willbe useful for most helium-neon, argon and krypton gas discharge lasers.For laser diodes and YAG lasers, a germanium photodetector whichmeasures wavelengths from 0.6 to 1.9 microns would be acceptable. Forhigh powered CO₂ lasers, a pyroelectric detector which operates on heatabsorption would be used. The pyroelectric detector has a broadwavelength range but is insensitive and requires a beam of 1 watt ormore in power to give adequate signals above its noise level.

As noted above, the width of the beam is derived by multiplying the timeperiod between two clip levels and the velocity of rotation of the hub.Therefore, in order to obtain accurate measurements, the speed ofrotation of the hub must be accurately controlled. This requirement ismet by using a stepping motor with a high step count (400 steps perrevolution) driven at a constant step rate. Alternately, a constantspeed motor corrected by a feedback loop may be used. For either means,maintaining a rim velocity accuracy constant to one-tenth of one percentis desirable.

It is also necessary to know the rotational position of the hub, tolocate the input beam position relative to the instrument, as discussedabove in connection with FIG. 13. This information is provided by usingsome form of optical encoding. Position information can also begenerated directly if the hub is driven using a high speed steppermotor.

FIG. 18 illustrates the preferred hub 134 and aperture format used inthis embodiment of the subject invention. As can be seen, this hubincludes one aperture 136 having two opposed 45° knife edges. A window138 is disposed opposite aperture 136 for passing light.

In the preferred embodiment, two pinholes 150,152 of different sizes areprovided for generating information about beam profiles. Windows(154,156) are aligned with pinholes 150,152 for transmitting the lightpassing therethrough. The use of the pinholes to obtain informationabout profiles is discussed below

The selection of the diameter of the hub is based on two opposingfactors. The first factor is a desire to create the largest differencebetween beam diameters at both the front and rear aperture positions oneither side of the hub. This argues for a large diameter hub. Thediameter of the hub must, however, be limited to insure that a constantrotation speed can be maintained without significantly increasing thesize and cost of the motor. As can be appreciated, as the hub diameteris increased, the torque needed to drive the hub increases. In fact, thepower rating of the motor scales with the hub diameter by a factor D³.It is believed that a good compromise is reached when a practical hubdiameter is selected (2 to 3 inches) together with the focal length ofthe lens such that the variation in beam diameter, measured at the frontand rear aperture positions, is at least on the order of the √2. The hubrotates at about a 10 Hz rate to give real-time measurements and stillallow sufficient time in each cycle for processor computations.

Due to the fact that the selection of some of the components is dictatedby the wavelength of the beam, at least two commercial models are beingconsidered. The selection of components is given below in Table I. Thefocal lengths and hub diameters listed produce a √2 or greater beam sizeincrease across the hub diameter, for an input beam diameter at the lensof 1/2 mm or greater. This minimum input beam diameter should permitmeasurements to be made on most commercial lasers.

                  TABLE I                                                         ______________________________________                                                         Model 1 Model 2                                              ______________________________________                                        Wavelength range (microns)                                                                       0.2-1.9   10.6                                             Focal length of lens                                                                             10 cm.    15 cm.                                           Detector type      Si or Ge  pyroelectric                                                        photocell detector                                         Hub diameter       2 inches  3 inches                                         ______________________________________                                    

Beam Alignment

As discussed above, by detecting the 50% transmission point past a pairof 45° knife edges, information about beam position can be derived. Inthe preferred embodiment of the subject invention, this information canbe provided to the user in a usable form with a graphic display shown inFIG. 16. The output of detector 130 is supplied to a microprocessorhoused in the stand alone console unit 190. Console unit 190 alsoincludes a display panel 192 which provides visual feedback of theinformation generated by the processor. A more detailed view of one formof display is shown in FIG. 19. This display includes a pair ofcoordinate plots giving X and Y information on the position of the beamat both the front and rear aperture positions. Information from thesetwo spaced apart locations provides position as well as alignmentinformation.

Referring back to FIG. 13, it will be recalled that X and Y coordinateinformation can be derived by noting the times and computing the timedifferences for the 50% cut points from the two knife edges. This X andY information can then be used to generate a spot on the displaycorresponding to the position of the beam within the instrument. Theuser can then adjust the optical axis of the instrument with respect tothe propagation axis of the laser beam until the displayed spots 206,208 are centered on each of the coordinate maps. For the display asshown, the foreground coordinate map 202 represent the input lens 132,and the input beam (when looking towards the lens) is seen to enter alittle below and to the left of center of the lens. In the rear map 204,the beam is seen to strike the detector in the rear of the instrument alittle high and to the right. The beam parameters displayed 210, 212 forthe two principal planes are calculated for the input beam, with theY-axis 212 highlighted indicating that is the primary principal plane(the lens is being servoed to focus that axis most critically on therear aperture position). The distance Z_(o) to the input waist ismeasured from the lens. The designation 10-FAR FIELD, 216, means theprofile shown is taken with a 10-micron diameter pinhole at the focused,rear aperture position as discussed below. The clip points used toanalyze the profile (which can be set by the user) are indicated at 218,and the profile width 220 is given as the far field full divergenceangle. The total power in the beam (appearing at 224) can be obtainedfrom the 100% transmission signals past the knife edges. The wavelength226 of the laser beam is initially entered into the instrument's memoryby the user, as this must be known for the processor to computer thebeam parameters via equation (11). Not shown in FIG. 19 are the parts ofthe display used to label the functions of the control buttons on theconsole unit 190. The functions and their labels change with theselection of the various operating modes.

The ability to provide such coordinate map positioning information isextremely desirable. Obviously, alignment of the beam prior to measuringits quality M² will facilitate obtaining consistent, reproducibleresults. The ability to provide alignment information provides otheradvantages.

One advantage is that the subject apparatus can be used to provideinformation about the alignment of optical elements that steer the laserbeam. Another important parameter of laser operation is referred to aspointing stability. This parameter defines the ability of the laser beamto point in a stable, fixed direction. The subject apparatus can beprogrammed to monitor, and store in memory the pointing drift from analigned position to provide the user with information on pointingstability.

Another advantage to providing position information is that it can beused to align the beam prior to obtaining a beam profile using thepinholes carried on the hub. More specifically, the typical focused beamsizes to be measured might have a diameter of about 100 microns.Accordingly, slight alignment errors can shift the plan line of thepinhole so that it will not cross the center of the beam or that it willmiss the focused beam entirely. In prior art devices using pinholes togenerate profiles, it often took many minutes of searching bytranslating the profiler on a translation stage to have the pinholeoverlap even a small portion of the beam so that a signal could begenerated, before centering could be effected by maximizing this signal.This problem is overcome in the subject invention since the beam can bealigned prior to seeking pinhole profile information by the knife edgescan information, as discussed previously.

Still another advantage to precise alignment is that it allows for anadditional measurement for quantifying the ability to tightly focus amultimode beam. The latter measurement is discussed below.

Beam Profiling

As mentioned above, it is possible to obtain the equivalent of aslit-profile of the beam if the transmission signal past the knife edgeis differentiated. This approach was suggested in the literature byArnuad, in the earlier cited reference.

In the preferred embodiment, however, maximum information about beamprofiles can be obtained using a pinhole scan. A pinhole is preferredbecause it most fully reveals the full structure of the mode of the beamand its use is made easy by the alignment information provided by theknife edges as discussed above.

The general use of a pinhole to obtain profile information is similar tothe prior art. As the pinhole passes through the beam, the detector willmeasure a variation in transmitted power which can be used to generate aprofile display of the type shown in FIGS. 1, 3A, 4A, 5A and 6A-C. Thisdata can be placed on a display associated with the device as shown inFIG. 19.

While the general approach for obtaining pinhole profile information issimilar to the prior art devices, there are a few important anddistinguishing differences. One of the most significant is that since alens is used to focus the beam, a far field profile, relatively free ofoverlaid diffraction patterns can be generated. More specifically, aspreviously discussed, the limiting aperture of a laser will typicallycreate diffraction effects which produce interfering distortions ofpinhole profiles taken in the near field of the laser beam. Most users,and particularly industrial users, are interested in the beam profile ata significant distance from the laser. In the past, unless the user setup his own lens and pinhole profiler on a translation stage, thisinformation was gotten by taking the profile far away from the laser. Asdescribed earlier, this requirement was often very inconvenient.

This problem is overcome in the subject device because the lensfunctions to put the pinhole aperture in the far field of thetransformed beam and effectively decouple the diffraction effects fromthe pinhole profiles. More specifically, the lens will focus thediffracted light, which radiates from the limiting aperture as itssource, at a different distance than the input beam waist. Accordingly,if the profile is taken at the transformed waist position, an effective"far field" profile will be generated. The automatic lens-focusing servoof the present instrument is a great convenience in setting up thisfar-field profile.

Where the subject device is actually located in the far field of theinput beam, there will be no diffraction/interference effects from thelaser limiting aperture. However, the beam will have a relatively largeinput diameter such that the focused beam will be quite small and may beso small as to cause convolution distortions of the pinhole profile evenwith the smaller pinhole diameter. In the latter case, it is desireableto obtain the profile at a point spaced from the focus of the lens. Thisresult can easily be achieved if the beam is focused close to the rearhub plane. The profile can then be taken with the pinhole at the frontaperture position. Since the processor knows the input beam parameters,in particular the input beam waist location and beam diameter at thelens, it may be programmed to display the front aperture positionprofile, when it calculates too large a convolution error for the rearaperture position. The indication 216 on the display, FIG. 19, wouldthen change to "10-AT LENS" or "50-AT LENS". This shows that the profileon the display was taken at the front aperture position, with either the10 micron or 50 micron diameter pinhole, and that the beam width scale220 (now changed to units of millimeters, mm, instead of milliradians,mr) shows the computed beam width at the lens 132. For every automaticmode of the instrument, where the processor makes a decision as to whatto display or how to take data, the user has the option to turn off theautomatic mode and make a manual selection.

In the preferred embodiment of the hub 134 shown in FIG. 18, twopinholes 150, 152 of different diameters are provided. The use of twodifferent diameter pinholes increases the ranges of input beam powersand diameters for which a pinhole-profile free of serious convolutionerrors can be obtained. As mentioned previously, for a profile accurateto 1% of the diameter of the beam at the aperture position, the pinholediameter should be less the 1/6 of this beam diameter. However, it isgenerally preferred to use the largest pinhole diameter meeting thisminimum convolution error criterion, as this passes the most beam powerand gives the highest signal to noise ratio for the profile. Theprocessor knows the transformed beam diameters at each aperture positionfrom the knife edge transmission measurements. Thus, the processor cancompute the convolution errors for the two aperture positions and theavailable pinhole diameters, and select for the display the combination(indicated at 216 in FIG. 19) giving the cleanest profile free ofconvolution error. Pinhole diameters in the range of 25 to 50 micronsfor the larger diameter, and in the range of 5 to 10 microns for thesmaller diameter, are believed to be adequate sizes to generate cleanpinhole profiles for a wide variety of beams from commercial lasers inthe present instrument.

Direct Measurement of the Focused Power Density of a Multimode Beam

Since the preferred embodiment of the invention includes a high quality,low aberration lens, a measurement of the focused power density of amultimode input beam can be performed. This measurement can be useful insome laser machining applications which might be sensitive to how muchlaser power can be delivered within a spot of a particular diameter, butnot sensitive to the way this power is distributed within that spotdiameter. A pinhole profile in this case might contain more informationthan is of interest to the user. In contrast, the user will want toobtain a direct measure of the fraction of the beam power which can befocused within the particular spot diameter.

Here the beam position detection and focus adjustment capabilities ofthe instrument can be utilized to set up the transformed beam in astandardized way, and to permit the introduction of an aperture intothis beam. The aperture size and shape is specified by the user and isscaled to function in the transformed beam in the same way the beam fromthe laser will function in the user's application. The transmissionthrough this aperture is computed from the full beam power (readout 224in FIG. 19) measured before and after introduction of the scaledaperture into the transformed beam. The standardized conditions mayconveniently be that the input beam is centered on both coordinate maps202 and 204, and the lens is positioned to put the transformed beamwaist at the center of the hub as previously described. Provision forinserting the scaled aperture 157, in plate 159, shown in FIG. 18 to thecentered beam position at the center of the hub can be provided in theinstrument. The translation and angular adjustments of the instrumentare peaked to maximize the transmitted power and insure that the scaledaperture is accurately centered on the beam. Because the transformedbeam is set up to have its waist at the location of the scaled aperture,the transmission measurement is made insensitive to axial positioningerrors of the aperture and hence it is more accurate.

Additional Computation Capabilities of the Instrument

The processor controlling the instrument may also be used to computeadditional properties about the input beam of interest to the user. Theconsole 190 contains standard RS232 and IEEE488 data buses, throughwhich the instrument processor can download data to a larger computerfor the more extensive computations. The on-board processor can deliverthe six propagation constants (2W_(o), Z_(o) and M² for each of the twoprincipal planes) of the input beam in real time to the user's owncomputer, to permit automatic analysis and control of the experimentswhich utilize the laser beam.

The second moment of the intensity distribution across the laser beam isone such property that can be computed and is of interest to some users.For this, the clean pinhole profile of the beam is digitized and storedin the instrument's memory. The processor first computes the firstmoment of this stored profile, i.e. the mean of the scanning pinhole'sposition, weighted by the transmitted power, in scanning across thebeam. Then, the second moment is computed. The second moment is the meanof the square of the difference between the scan position, and the meanposition, weighted by the transmitted power in scanning across the beam.(These are the standard mathematical definitions for the first twomoments of any distribution function). Twice the square root of thesecond moment of the profile is called the root-mean-square beamdiameter. This quantity is of interest firstly in determining theparticular mixture of higher order modes in a multimode beam with aknown value of M². Secondly, it is of theoretical interest inunderstanding the way the higher-order-mode beam was generated in thelaser. Thirdly, the root-mean-square beam diameter may be shownmathematically to be an alternate definition for the beam diameter of amultimode beam, which is free of the types of discontinuities discussedwith regard to other definitions. This is because the root-mean-squarediameter is based on an integration over the whole beam cross-sectionand takes account of the total power in the beam.

Another computed property of interest to some users would be the totalpower in the input beam P, divided by the beam quality, or P/M². This isessentially a measure proportional to the peak intensity of the beam. Ifthe diameter of the internal limiting aperture in the laser is varied aswas described in connection with FIG. 11, to vary simultaneously boththe M² and the power P of the laser beam, a measurement in real time ofthe quantity P/M² would be of interest as there are applications oflasers which are primarily sensitive to the peak intensity of the beam.Accordingly, the processor can be programmed to compute this quantityfrom other measurements already described, and display the result at 224in FIG. 19. The units displayed in the latter case changed to W/M² todistinguish the result from the case where the total power is displayed.

It will also be of value to the instrument's user, to be able to enter alocation into the instrument (a given distance away from the lens 32)and have the processor calculate the beam diameter at that location. Theprocessor does this from the measured input beam parameters, usingequation (11). Thus, computed information about the behavior of the beamat inaccessible locations (such as inside a vacuum chamber) is providedin a rapid and useful fashion.

Finally, the user can download the beam parameters from the instrument'sprocessor into his own host computer, and by ray matrix methods known inthe literature, calculate the propagation and beam parameters of hismultimode beam at any point through a specified, arbitrary opticalsystem. This is one of the goals set forth in the section on thebackground to this invention.

First Alternate Embodiment

FIG. 20 illustrates another embodiment 200 of the subject invention.This embodiment incorporates one of the other approaches used in theprior art for measuring beam diameter.

As in the first embodiment, a lens 232 is used to create a transformedor imaged waist. Some means 236 is provided for translating the positionof the lens with respect to the detector portion 240 cf the device.

The diameter of the beam is measured by passing an aperture (a pinholeor a slit 242 mounted to cover the detector) through the beam. Theaperture and detector are translated past the beam using a linear arm246 driven by a stepper motor 248. For simplicity, a slit aperture isdiscussed below. A pinhole could be used similarly, with the addition ofa translation stage to center the pinhole scan line on the beam (notshown). The transmission past the slit is measured by the detector. Theoutput of the detector can be used to directly generate profileinformation of the type previously shown. The beam diameter can bederived using any one of the definitions discussed above where a cliplevel is set and the time elapsed between the clip levels can be used toderive the beam width.

As with the previous embodiment, the first step to determining thequality of the mode of the laser beam is to determine the location ofthe transformed waist. The waist is located by adjusting the position ofthe lens while continuously monitoring the diameter of the beam crossingthe slit. When the diameter is at a minimum, the beam waist is locatedin the plane of the slit and the diameter is recorded.

After the beam waist is located, the beam diameter at another knownlocation must be measured. In the illustrated embodiment, a portion ofthe beam 10a is split from the main beam 10 using a beam splitter 252.This portion of the beam is then redirected to the detector by a foldmirror 254. The beam diameter is then derived by measuring the powertransmitted past the slit as the arm extends into this second beam.

Since the portion 10a of the beam does not pass through the lens, thechange in input beam diameter as it traverses the known, relativelyshort, distance between the beam splitter 252 to the slit detector willbe very small. The processor first computes M² assuming that themeasured diameter of the beam 10a is the same as the beam diameter atthe lens. Thus, a beam diameter at the waist, and at one other knownlocation in the same beam (the transformed beam) are available tocalculate the input beam parameters to the first order as describedbefore. Knowing these parameters, the processor can then compute thesecond order corrections to these parameters, to take into account theslight difference in propagation path length of beam 10a between thebeam splitter 252 and the detector.

The advantage to using the device shown in FIG. 20 is that it is ofsimpler construction. However, it is believed that the primaryembodiment is more useful because of the greater amount of informationgenerated more rapidly since more apertures can be carried smoothly andprecisely at high speed through the beam.

Second Alternate Embodiment

FIG. 21 illustrates still another embodiment 300 of a device forcarrying out the subject invention. As in all the embodiments, atranslatable lens 332 is provided for creating and moving a transformedbeam waist. In this embodiment, the means for measuring the beamdiameter includes a spinning wire 342 driven by a motor 343. Thespinning wire moves through the path of the laser beam. Light reflectedoff the wire (shown at 346,348) is measured by detectors 356,358 andused to derive information about beam diameter. This method of takingtwo-axis beam profiles is described in the literature; Lim and Steen, J.Phys. E., (Sci. Inst.) Vol. 17, 1984, pp. 999-1007.

In accordance with the subject method, the position of the lens is movedalong the beam axis (shown at 360) in order to place the beam waist inthe plane of the spinning wire. The diameter of the waist is measured asin the literature reference above. The diameter of the beam at anotherknown location is obtained in the illustrated embodiment, by sliding thelens out of the beam (shown at 362). Thus, beam diameters at the waistand one other known location are obtained in a manner similar to thefirst alternate embodiment, and the beam parameters can be derivedsimilarly from this information.

Since this second alternative embodiment involves a reciprocating motion362 of the lens to perform the M² measurement, it is believed that theprimary embodiment is more useful once again, because more informationabout the beam is obtained more rapidly.

Specific Applications for Mode Quality Information

In planning laser material processing applications, prediction of thediameter of the beam-surface interaction region of a given input beamdiameter and lens focal length require a knowledge of M². High beamquality is essential where small focus-spot diameter is important.

Many laser applications require delivery of the beam over long andvariable length optical paths. An example is shown in FIG. 22. In thisdevice, a gantry beam delivery system is utilized to scan the beam 400over the workpiece 401 while the laser 402 remains stationary. The finaldelivery assembly 403 (consisting of a beam-bender and lens) will moveover a large range L, typically from a few meters to 20 meters from thelaser.

The most economical design for such an optical system uses opticalcomponents of the smallest possible diameter consistent with allowingthe entire beam to pass without significant aperture loss. Thisconstraint requires that a beam waist 404 of optimum diameter bepositioned in the middle of the variable portion of the optical path, ata distance L/2 from each end of the travel. In order to minimize thebeam diameters at the ends of the variable path, the optimum beam waistdiameter D₀ at location L/2 is given by: ##EQU5## Following thisapproach the diameter at each end will be larger than the diameter ofthe waist by a factor of √2. These diameters improve (decrease) as thebeam quality improves, if only as the square root of the beam qualitynumber M².

The beam 405 emitted by the laser is unlikely to have thecharacteristics required by Equation 18. To transform the laser beaminto the required beam will require the use of an optical systemreferred to in the literature as a mode-matching telescope. This opticalsystem is represented as the combination of lenses 406 and 407 in FIG.22. One or both of these lenses could be high reflectivity mirrors withsuitably curved surfaces. (It should be understood that the lenses shownin connection with the measurement apparatus described above could, aswell, be suitably-curved, high reflectivity mirrors.)

For laser applications requiring beam delivery over a fixed distance thesame relationship applies for minimizing optics diameter at the outputend 420 as shown in FIG. 23. This is especially true for articulatedoptical pipes (articulated arms) where there is often high interest inhaving a long arm and also having a small tube diameter at the far(distal) end to make it light and easy to manipulate. The maximumdistance L_(max) at which a beam waist can be positioned beyond anaperture large enough to pass a beam with diameter D is given by:

    L.sub.max =πD.sup.2 /(8M.sup.2 λ)                (19)

If this constraint the beam diameter at the output end will be D/√2. Asdescribed above, a modematching means will likely be required.

An instrument for measuring mode quality will be of use in finding andcorrecting aberrating elements in a laser optical system. As a firstexample, M² measurements were used as a quality control method on anassembly line building articulated arms (mentioned above) for thedelivery of a surgical laser beam. These arms consist of a series ofpipes, joined at the elbows by plane mirrors in mechanical assemblies(called knuckles) that keep the beam pointed down the center of the nextpipe, despite the motions of the whole arm necessary to deliver the beamto the desired target. It was found that the M² value for a beamtransmitted through a properly assembled arm was 1.1, little changedfrom the M² of the beam propagating in free space. However, when thesurface of one of the plane mirrors was distorted, (by overtighteningthe mounting screws) the M² value rose to 1.7. A simple profile of thetransmitted beam at one location might not have detected the aberration.Measurements of M² before and after the arm can accomplish this becausea change represents a change in beam quality caused by something in thepropagation path.

It is well known in optics textbooks that the aberrations of a lens usedto focus a beam depend on the orientation of the lens in the beam. Forinstance, a lens which has one plane and one spherical surface (aplano-convex lens), has less spherical aberration if the curved surfaceof the lens faces the (nearly) planar wavefronts of the collimated beam(instead of the converging spherical wavefronts of the focused beam). Ifthe lens is used at a large enough aperture that its sphericalaberration is significant, enlarging the spot size of the focus of thebeam, beam quality measurements would reveal the inadvertent reversal ofthe lens.

Thus, it is envisioned that beam quality instruments will be in routineuse for locating and correcting aberrating elements in a optical system.The useful property of M² here is that like the classical "diffractionlimit", beam quality is conserved (unchanged) in passage through(transmission or reflection) a non-aberrating system and increasesthrough an aberrating one. It is useful to define the aberrating qualityQ_(A) of an optical element for a beam of quality M² _(IN) as

    Q.sub.A =(M.sup.2.sub.OUT /M.sup.2.sub.IN)                 (20 )

where M² _(OUT) is the beam quality measured after traversal of theoptic. Q_(A) will generally depend on the diameter and M² of the inputbeam and increase with an increase in either, as can be appreciated inview of the above discussion relating to spherical aberration. For asystem of cascaded elements, all of low aberration, the overall Q_(A)will be the product of those for the individual elements as can be seenfrom equation (20). When a badly aberrating element is included in thecascade, M² increases upon exiting that element, which generallyincreases the aberrating qualities of the remaining elements in thecascade in a compounding fashion. It is evident that a beam qualityinstrument, applied to aberrating quality measurement will be ofconsiderable use in the testing of optical systems.

By the laws of light propagation and definition of beam quality, thevalue of M² can be no smaller than unity. An element might act on a beamto reduce its value of M², but never to less than one. A passive deviceknown as a spatial filter, for example, is intended to improve thequality of a beam. The beam is brought to a focus with a high qualitymicroscope objective, and at the focus there is placed a centeredpinhole of a diameter chosen to pass about 95% of the associatedfundamental mode for the input beam. This diameter is small enough toblock a considerable amount of the higher order mode content of thebeam, and the transmitted beam quality improves. Thus, the Q_(A) for thespatial filter is a number smaller than one. A beam quality instrumentcan therefore be used to adjust the alignment of a spatial filter for alower Q_(A) value.

Similarly, some active optical systems may have aberrating qualities ofless than unity, where the output beam quality is improved. In theeffect known as second harmonic generation, a laser beam typically inthe visible wavelength range is focused into a crystal having certainspecial properties, and an output beam having a wavelength of half thatof the input beam is generated, in the ultraviolet wavelength range. Theconversion efficiency of visible to ultraviolet is mode dependent, lowerorder modes generally producing higher conversions. It is thereforegenerally expected that the M² number for the second harmonic beam willbe lower than for the visible pump beam, indicating better beam qualityfor the second harmonic beam. Light propagation in the crystal can,however, also produce aberrations (which also differ in the twoprincipal planes of the beams) due to double refraction (the "walk-off"effect). Thus, the aberrating quality of a second harmonic crystal is aninteresting quality to measure. It is evident that once a beam qualityinstrument is widely available it will be of considerable use foraberrating quality analysis of laser physics experiments.

Beam quality instruments will also find applications in the set-up andadjustment of the laser system itself. An example where beam quality hasbeen used to do this was in a dye-laser photocoagulation system.Photocoagulation is the application of an intense burst of light, heredelivered through a fiber, to treat diseases of the eye. Dye lasersproduce output beams whose wavelength can be varied or tuned, but theytypically require another laser, here an argon ion laser, to opticallyactivate or pump the dye molecules. The dye laser is used for treatmentbecause by tuning the wavelength, selective absorption can be had in theproper tissue in the eye.

The conversion efficiency from ion laser pump beam power, to dye laseroutput beam power, is dependent on the beam qualities of both beams. Thelowest acceptable beam quality of the dye laser beam was fixed by therequirement for transmission of this beam through the delivery fiber.This system is an example of the "power vs. mode" trade off discussed inthe background section of the application. Various optics combinationswere tried inside the ion laser resonator, which produced coupledchanges in the ion laser pump beam power and mode. The effect of thesechanges on the dye laser output beam power (of acceptable beam quality)were monitored. It was found that reducing the M² value for the ionlaser beam from M² =6.3 to M² =3.2 decreased the ion beam power onlyslightly, but further reduction to M² =1.4 dropped this power by 20%.The dye laser power, on the other hand, rose by +45% over the originalvalue with the first change, then fell from this peak to +35% over theoriginal value with the second change. Thus beam quality measurementswere successfully used to optimize this complex problem of trading-offpower versus mode.

A simpler example of beam quality use in adjustment of a laser is insetting up the internal limiting aperture (selecting its diameter, andcentering its position), and in aligning the resonator mirrors, to givea desired M² value. This is the classic example of the power-vs.-modetrade-off. An off-center or incorrectly sized aperture, coupled with aslightly misaligned mirror, may produce the expected power, but in apoorly focusable mode. Without an instrument to quantify the modequality, the unfortunate technician left to do the set-up is apt to erron the side of the variable he can measure, and ship a laser which meetspower specifications, but will not meet customer expectations. This isone of the problems which motivated the present work and led to thepresent invention.

While the subject invention has been described with reference to thepreferred embodiments, various changes and modifications could be madetherein, by one skilled in the art, without varying from the scope andspirit of the subject invention as defined by the appended claims.

We claim:
 1. An apparatus for determining the input alignment of a laserbeam with respect to the apparatus comprising:lens means for focusingthe beam and creating a transformed beam waist; a rotatable hub of aknown diameter located in the path of the laser beam at a known distancefrom the lens means and having at least two apertures formed therein fortransmitting the beam, with one of said apertures including a pair ofopposed knife edges each disposed perpendicularly with each other and ata 45° angle with respect to the plane of rotation of the hub; means formeasuring the power of the beam transmitted through said apertures andpast said knife edges, said means being located outside the hub oppositeto the incoming laser beam; and processor means connected to saidmeasuring means, said processor means for determining the center of thetransformed beam in two transverse orthogonal directions and at twoopposed sides of the hub based upon variations in transmitted power,said processor means further determining the alignment of the input beambased on the focal length of the lens means, the determined transformedbeam centers, the known diameter of the hub and the known distance fromthe hub to the lens means.
 2. An apparatus as recited in claim 1 whereinsaid processor means determines the position of the center of the beamat each knife edge based upon the time when power transmitted past theknife edges is equal to 50 percent of maximum.
 3. An apparatus asrecited in claim 1 further including a means for displaying the positionof the beam calculated by the processor means.
 4. An apparatus asrecited in claim 1 further including a means for adjusting the positionof the hub so that the propagation axis of the beam is aligned with theoptical axis of the apparatus.
 5. An apparatus as recited in claim 1wherein the input alignment of the beam is repeatedly monitored andstored to provide a record of the pointing drift of the beam over time.6. An apparatus for determining the input alignment of a laser beam withrespect to the apparatus comprising:lens means for focusing the beam andcreating a transformed beam waist; a rotatable support carrying anaperture for transmitting the beam, said support functioning totranslate the aperture through the transformed beam at two differentlocations a known distance apart along the propagation axis thereof anda known distance from the lens means; means for measuring the power ofthe beam transmitted through said aperture, with said measuring meansbeing located beyond said two locations in the beam path; and processormeans connected to said measuring means, said processor means fordetermining the center of the transformed beam at said two locations inthe beam path based upon variations in the measured transmitted power,said processor means further determining the alignment of the input beambased on the focal length of the lens means, the determined transformedbeam centers and the known distances between the two locations and thelens means.
 7. An apparatus as recited in claim 6 wherein said apertureincludes a knife edge disposed at an angle with respect to the plane ofrotation of the support.
 8. An apparatus as recited in claim 7 whereinsaid aperture includes a second knife edge disposed at an angle withrespect to the plane of rotation of the support and wherein said firstand second knife edges are not parallel.
 9. An apparatus as recited inclaim 8 wherein said first and second knife edges are perpendicular. 10.An apparatus as recited in claim 9 wherein said first and second knifeedges are disposed at a 45 degree angle with respect to the plane ofrotation of the support.
 11. An apparatus as recited in claim 10 whereinsaid processor means determines the position of the center of the beambased upon the time when the power transmitted past the knife edges isequal to 50 percent of maximum.
 12. An apparatus as recited in claim 11further including a means for displaying the position of the beamcalculated by the processor means.
 13. An apparatus as recited in claim12 further including a means for adjusting the position of the supportso that the propagation axis of the beam is aligned with the opticalaxis of the apparatus.
 14. An apparatus as recited in claim 6 whereinthe input alignment of the beam is repeatedly monitored and stored toprovide a record of the pointing drift of the beam over time.